Smoothness of Metropolis-Hastings algorithm and application to entropy estimation

Didier Chauveau; Pierre Vandekerkhove

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 419-431
  • ISSN: 1292-8100

Abstract

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The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent nonparametric estimate of the entropy for these iterative densities. This theoretical study can be viewed as a building block for a more general MCMC evaluation tool grounded on such estimates.

How to cite

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Chauveau, Didier, and Vandekerkhove, Pierre. "Smoothness of Metropolis-Hastings algorithm and application to entropy estimation." ESAIM: Probability and Statistics 17 (2013): 419-431. <http://eudml.org/doc/273622>.

@article{Chauveau2013,
abstract = {The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent nonparametric estimate of the entropy for these iterative densities. This theoretical study can be viewed as a building block for a more general MCMC evaluation tool grounded on such estimates.},
author = {Chauveau, Didier, Vandekerkhove, Pierre},
journal = {ESAIM: Probability and Statistics},
keywords = {entropy; Kullback divergence; Metropolis-Hastings algorithm; nonparametric statistic},
language = {eng},
pages = {419-431},
publisher = {EDP-Sciences},
title = {Smoothness of Metropolis-Hastings algorithm and application to entropy estimation},
url = {http://eudml.org/doc/273622},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Chauveau, Didier
AU - Vandekerkhove, Pierre
TI - Smoothness of Metropolis-Hastings algorithm and application to entropy estimation
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 419
EP - 431
AB - The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent nonparametric estimate of the entropy for these iterative densities. This theoretical study can be viewed as a building block for a more general MCMC evaluation tool grounded on such estimates.
LA - eng
KW - entropy; Kullback divergence; Metropolis-Hastings algorithm; nonparametric statistic
UR - http://eudml.org/doc/273622
ER -

References

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